Several methods for dividing one quantity by another, or for determining the inverse of a quantity are known. They include:
(a) Subtracting the divisor from the dividend repetitively until the remainder is less than the divisor;
(b) Repetitive subtraction with shifting after determination of each quotient digit;
(c) Subtraction of prestored divisor multiples from dividend, with shifting;
(d) Approximation by another function, e.g., power series.
The known methods are disclosed, e.g., in U.S. Pat. Nos. 3,631,230, 3,684,038 and 4,084,254, and in an article "Approximating division by a constant" by R. L. Ho, IBM Technical Disclosure Bulletin, Vol. 22, No. 4, September 1979, pp. 1554-1557.
A major problem in the design of arithmetic circuitry, particularly for division, is that with a given accuracy of the circuitry or technique, only a limited range of variables can be handled. For variables at the margin or outside of that range, no useful results can be obtained because the errors may be too large. Increased accuracy can only be obtained at the cost of more expensive hardware, or duplication of certain arithmetic elements, or by slower operation of the circuitry due to an increase in the number of repetitive operations.